KE = (3/2) * k * T
Where:
* KE is the mean translational kinetic energy
* k is the Boltzmann constant (1.38 × 10⁻²³ J/K)
* T is the absolute temperature in Kelvin
Key points:
* Translational kinetic energy refers to the energy associated with the motion of molecules from one point to another.
* This equation applies to ideal gases, where intermolecular forces are negligible.
* The equation implies that as the temperature increases, the average speed of the gas molecules increases, and hence, the kinetic energy also increases.
Example:
Let's say the temperature of a gas is 300 K. Then, the mean translational kinetic energy of the gas molecules would be:
KE = (3/2) * (1.38 × 10⁻²³ J/K) * (300 K)
KE ≈ 6.21 × 10⁻²¹ J
Note: The mean translational kinetic energy is an average value. Individual gas molecules will have different kinetic energies, but the average will follow this relationship with temperature.
